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Search results for: MARCINKIEWICZ AVERAGE · SMOOTH ORTHOGONAL PROJECTION · HESTENES OPERATOR · PARSEVAL FRAME
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Marcinkiewicz Averages of Smooth Orthogonal Projections on Sphere
PublicationWe construct a single smooth orthogonal projection with desired localization whose average under a group action yields the decomposition of the identity operator. For any full rank lattice \Gamma ⊂ R^d , a smooth projection is localized in a neighborhood of an arbitrary precompact fundamental domain R^d / \Gamma. We also show the existence of a highly localized smooth orthogonal projection, whose Marcinkiewicz average under the...
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Harmonic Analysis
Open Research DataWe construct a decomposition of the identity operator on a Riemannian manifold M as a sum of smooth orthogonal projections subordinate to an open cover of M. This extends a decomposition on the real line by smooth orthogonal projection due to Coifman and Meyer (C. R. Acad. Sci. Paris, Sér. I Math., 312(3), 259–261 1991) and Auscher, Weiss, Wickerhauser...
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Parseval Wavelet Frames on Riemannian Manifold
PublicationWe construct Parseval wavelet frames in L 2 (M) for a general Riemannian manifold M and we show the existence of wavelet unconditional frames in L p (M) for 1 < p < ∞. This is made possible thanks to smooth orthogonal projection decomposition of the identity operator on L 2 (M), which was recently proven by Bownik et al. (Potential Anal 54:41–94, 2021). We also show a characterization of Triebel–Lizorkin F sp,q (M) and Besov B...
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Smooth orthogonal projections on sphere.
PublicationWe construct a decomposition of the identity operator on the sphere S^d as a sum of smooth orthogonal projections subordinate to an open cover of S^d. We give applications of our main result in the study of function spaces and Parseval frames on the sphere.
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Smooth Orthogonal Projections on Riemannian Manifold
PublicationWe construct a decomposition of the identity operator on a Riemannian manifold M as a sum of smooth orthogonal projections subordinate to an open cover of M. This extends a decomposition on the real line by smooth orthogonal projection due to Coifman and Meyer (C. R. Acad. Sci. Paris, S´er. I Math., 312(3), 259–261 1991) and Auscher, Weiss, Wickerhauser (1992), and a similar decomposition when M is the sphere by Bownik and Dziedziul (Const....
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The asymptotic formula for the error in orthogonal projection
PublicationW pracy podano formułę asymptotyczną błędu aproksymacji dla rzutów ortogonalnych w normie L^p.
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Comparison of the fracture toughness of pine wood determined on the basis of orthogonal linear cutting and frame sawing
PublicationIn this paper, the values of the fracture toughness of Scots pine determined by cutting tests are presented. The cutting tests were carried out using the samples of Scotch pine (Pinus sylvestris L.) from Pomeranian Region, Poland. These experiments were carried out on two research stands: orthogonal linear cutting tests were conducted using the microtome instrument and the frame saw PRW-15M was used for sawing tests. The values...
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A Noether theorem for stochastic operators on Schatten classes
PublicationWe prove that a stochastic (Markov) operator S acting on a Schatten class C_1 satisfies the Noether condition S'(A) = A and S'(A^2) = A^2, where A is a Hermitian bounded linear operator on a complex Hilbert space H, if and only if, S(E(G)XE(G)) = E(G)S(X)E(G) holds true for every Borel subset G of the real line R, where E(G) denotes the orthogonal projection coming from the spectral resolution of A. Similar results are obtained...
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Macromodeling techniques for accelerated finite element analysis
PublicationThis paper deals with the Model Order Reduction applied locally in the Finite Element Method (FEM) analysis. Due to the reduction process, blocks of FEM system matrices associated with selected subregions of the computational domain are projected onto the subspaces spanned by the vectors of suited orthogonal projection basis. In effect, large and sparse FEM matrices are replaced with small and dense ones, called macromodels. This...
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A Subspace-Splitting Moment-Matching Model-Order Reduction Technique for Fast Wideband FEM Simulations of Microwave Structures
PublicationThis article describes a novel model-order reduction (MOR) approach for efficient wide frequency band finite-element method (FEM) simulations of microwave components. It relies on the splitting of the system transfer function into two components: a singular one that accounts for the in-band system poles and a regular part that has no in-band poles. In order to perform this splitting during the reduction process, the projection...
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Compressed Projection Bases for Model-Order Reduction of Multiport Microwave Components Using FEM
PublicationThis paper presents a projection basis compression technique for generating compact reduced-order models (ROM) in the FE analysis of microwave devices. In this approach redundancy is removed from the projection basis by means of the proper orthogonal decomposition technique applied to the projected system of linear equations. Compression allows for keeping the size of a reduced-order model as small as possible without compromising...
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Scattering From a Cylindrical Object of Arbitrary Cross Section With the Use of Field Matching Method
PublicationA simple and intuitive solution to scattering problems in shielded and open structures is presented. The main idea of the analysis is based on the direct field matching technique involving the usage of projection of the fields at the boundary on a fixed set of orthogonal basis functions. Different convex shapes and various obstacle materials are considered to verify the validity of the method in open and closed structures. The...
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Macromodels for efficient FEM simulations of waveguides and resonators
PublicationThis paper introduces a novel technique for enhancing the efficiency of the finite element method (FEM) by incorporating special modules, called macromodels, into the standard eigenvalue formulation. The number of unknowns in the separated macromodel subdomain can be significantly reduced by orthogonal projection, using the efficient nodal order reduction algorithm. The idea of macromodels implementation is demonstrated on a simple...
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Ultrashort Opposite Directed Pulses Dynamics with Kerr Effect and Polarization Account
PublicationWe present the application of projection operator methods to solving the problem of the propagation and interaction of short optical pulses of different polarizations and directions in a nonlinear dispersive medium. We restrict ourselves by the caseof one-dimensional theory, taking into account material dispersion and Kerr nonlinearity. The construction of operators is delivered in two variants: for the Cauchy problem and for the...
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Propagation in the Open Cylindrical Guide of Arbitrary Cross Section With the Use of Field Matching Method
PublicationA simple solution to propagation problem in open waveguides and dielectric fibers of arbitrary convex cross section is presented. The idea of the analysis is based on the direct field matching technique involving the usage of the field projection at the boundary on a fixed set of orthogonal basis functions. A complex root tracing algorithm is utilized to find the propagation coefficients of the investigated guides. Different convex...
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Scattering and Propagation Analysis for the Multilayered Structures Based on Field Matching Technique
PublicationA semi-analytical method is employed to the analysis of scattering and guiding problems in multilayer dielectric structures. The approach allows to investigate objects with arbitrary convex cross section and is based on the direct field matching technique involving the usage of the field projection at the boundary on a fixed set of orthogonal basis functions. For the scattering problems the scattered field in the far zone is calculated...
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Generalized Gradient Equivariant Multivalued Maps, Approximation and Degree
PublicationConsider the Euclidean space Rn with the orthogonal action of a compact Lie group G. We prove that a locally Lipschitz G-invariant mapping f from Rn to R can be uniformly approximated by G-invariant smooth mappings g in such a way that the gradient of g is a graph approximation of Clarke’s generalized gradient of f . This result enables a proper development of equivariant gradient degree theory for a class of set-valued gradient...
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The generalization by simplification operator with Sester’s method of objects representing groups of buildings in Gdańsk district - scale 1:10000. Data from OSM
Open Research DataThe process of automatic generalization is one of the elements of spatial data preparation for the purpose of creating digital cartographic studies. The presented data include a part of the process of generalization of building groups obtained from the Open Street Map databases (OSM) [1].
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An extended basis inexact shift–invert Lanczos for the efficient solution of large-scale generalized eigenproblems
PublicationThis paper proposes a technique, based on the Inexact Shift–Invert Lanczos (ISIL) method with Inexact Jacobi Orthogonal Component Correction (IJOCC) refinement, and a preconditioned conjugate-gradient (PCG) linear solver with multilevel preconditioner, for finding several eigenvalues for generalized symmetric eigenproblems. Several eigenvalues are found by constructing (with the ISIL process) an extended projection basis. Presented...
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Scene Segmentation Basing on Color and Depth Images for Kinect Sensor
PublicationIn this paper we propose a method for segmenting single images from Kinect sensor by considering both color and depth information. The algorithm is based on a series of edge detection procedures designed for particular features of the scene objects. RGB and HSV color planes are separately analyzed in the first step with Canny edge detector, resulting in overall color edges mask. In depth images both clear boundaries and smooth...
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The generalization by simplification operator with Sester’s method of objects representing groups of buildings in Kartuzy district - scale 1:10000. Data from OSM
Open Research DataThe process of automatic generalization is one of the elements of spatial data preparation for the purpose of creating digital cartographic studies. The presented data include a part of the process of generalization of building groups obtained from the Open Street Map databases (OSM) [1].
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Developing students' spatial skills and teaching the history of architecture through structural drawing
PublicationThe method of “structural drawing" is used in teaching history of architecture in the Architectural Faculty of Gdańsk University of Technology. It is addressed to students of the first semester of study – so to the architectural beginners. There are three main goals of the structural drawing method used in that educational course: (1) developing the students’ spatial skills; (2) training architectural drawing ability; (3) teaching...
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The Use of Photographs in the Teaching/Learning of Descriptive Geometry
PublicationThe article presents the concept of enriching the Descriptive Geometry course with photographs and several simplified real-life engineering tasks. The photographic images used for the exercises are tightly linked to engineering structures, the given specialization and the surrounding world. The photo image as a record of central projection of a real space can be useful for presentation and analysis of the properties of perspective....
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Error analysis of calculating average d-q current components using Regular Sampling and Park transformation in FOC drives
PublicationIn electric drives using voltage source inverters, motor currents contain ripple component resulting from pulse-width modulated (PWM) voltage. The frequency range of the ripples is much higher than the bandwidth of current control. Therefore the control is performed on the basis of a fundamental current component, i.e. average value with the averaging time being the PWM period. In majority of cases the average current is measured...
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Efficient analysis of structures with rotatable elements using model order reduction
PublicationThis paper presents a novel full-wave technique which allows for a fast 3D finite element analysis of waveguide structures containing rotatable tuning elements of arbitrary shapes. Rotation of these elements changes the resonant frequencies of the structure, which can be used in the tuning process to obtain the S-characteristics desired for the device. For fast commutations of the response as the tuning elements are rotated, the...
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The generalization by simplification operator with Sester’s method of objects representing groups of buildings in Kartuzy district - scale 1:10000
Open Research DataThe process of automatic generalization is one of the elements of spatial data preparation for the purpose of creating digital cartographic studies. The presented data include a part of the process of generalization of building groups obtained from the national geodesy and cartography resource from BDOT10k (10k topographic database) [1].
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The generalization by simplification operator with Sester’s method of objects representing groups of buildings in Gdańsk district - scale 1:10000
Open Research DataThe process of automatic generalization is one of the elements of spatial data preparation for the purpose of creating digital cartographic studies. The presented data include a part of the process of generalization of building groups obtained from the national geodesy and cartography resource from BDOT10k (10k topographic database) [1].
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The generalization by simplification operator with Sester’s method of objects representing groups of buildings in Kartuzy district - scale 1:25000
Open Research DataThe process of automatic generalization is one of the elements of spatial data preparation for the purpose of creating digital cartographic studies. The presented data include a part of the process of generalization of building groups obtained from the national geodesy and cartography resource from BDOT10k (10k topographic database) [1].
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A Method of MOS Evaluation for Video Based Services
PublicationThis paper deals with a method for QoE evaluation for the services transmitting large amount of data perceived by the end user in relatively short time periods, e.g. streaming video in mobile operator...
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Using phase of short-term Fourier transform for evaluation of spectrogram performance
PublicationThe concept of spectrogram performance evaluation which exploits information on phase of short-term Fourier transform (STFT) is presented. A spectrograph which is time-frequency analyzing tool, is compared to a filter bank that demultiplexes a signal. Local group delay (LGD) and channelized instantaneous frequency (CIF) is obtained for each filtered component signal. In presented solution the performance is evaluated using so-called...
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Efficient Usage of Dense GNSS Networks in Central Europe for the Visualization and Investigation of Ionospheric TEC Variations
PublicationThe technique of the orthogonal projection of ionosphere electronic content variations for mapping total electron content (TEC) allows us to visualize ionospheric irregularities. For the reconstruction of global ionospheric characteristics, numerous global navigation satellite system (GNSS) receivers located in different regions of the Earth are used as sensors. We used dense GNSS networks in central Europe to detect and investigate...
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Dead time effects compensation strategy by third harmonic injection for a five-phase inverter
PublicationThis paper proposes a method for compensation of dead-time effects for a fivephase inverter. In the proposed method an additional control subsystem was added to the field-oriented control (FOC) scheme in the coordinate system mapped to the third harmonic. The additional control loop operates in the fixed, orthogonal reference frame ( α - β coordinates) without the need for additional Park transformations. The purpose of this method...
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Performance analysis of data transmission in MC-CDMA radio interface with turbo codes
PublicationMulti-carrier code division multiple access (MC-CDMA) technique is a combination of two radio access techniques: CDMA and orthogonal frequency division multiplexing and has the advantages of both techniques. The paper presents the design of transmitter and receiver for MC-CDMA radio interface. It also presents encoders and decoders of turbo codes which were used in simulation of the MC-CDMA technique. Two turbo codes with 8-state...
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Rectangular Waveguide Filters Based on Deformed Dual-Mode Cavity Resonators
PublicationIn this paper, a novel design for rectangular waveguide filters with deformed dual-mode (DM) cavity resonators is demonstrated. The new resonant cavity shape is a result of applying shape deformation to the basic rectangular cavity to enable its dual-mode operation. Internal coupling between the two orthogonal cavity modes is realized by geometry deformation, eliminating the need for additional coupling elements. The designs are...
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Face Profile View Retrieval Using Time of Flight Camera Image Analysis
PublicationMethod for profile view retrieving of the human face is presented. The depth data from the 3D camera is taken as an input. The preprocessing is, besides of standard filtration, extended by the process of filling of the holes which are present in depth data. The keypoints, defined as the nose tip and the chin are detected in user’s face and tracked. The Kalman filtering is applied to smooth the coordinates of those points which...
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Horizontal velocity field derived from EPN and ASG-EUPOS satellite data on the example of south-western part of Poland
PublicationPresently the determination of the velocity field in the global reference frame is possible by using different space techniques and dense terrestrial networks from global to local and regional scales. However, the reliability of such determinations is strongly limited by the restricted number of unmodeled effects. Some of them are periodic (atmospheric or hydrological effects), some instantaneous (natural or man-made seismicity)...
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Estimation of Average Speed of Road Vehicles by Sound Intensity Analysis
PublicationConstant monitoring of road traffic is important part of modern smart city systems. The proposed method estimates average speed of road vehicles in the observation period, using a passive acoustic vector sensor. Speed estimation based on sound intensity analysis is a novel approach to the described problem. Sound intensity in two orthogonal axes is measured with a sensor placed alongside the road. Position of the apparent sound...
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Testing OFDM Transmission Schemes for Shallow Water Acoustic Communications
PublicationLarge variability of communication properties of underwater acoustic channels, and especially strongly varying instantaneous conditions in shallow waters, is a tough challenge for the designers of underwater acoustics communication (UAC system. There is a need for developing adaptive signaling schemes that would dynamically optimize signal parameters in both physical and link layers of communication protocols. The orthogonal frequency...
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Metoda analizy wielokryterialnej do planowania rozwoju sieci elektroenergetycznej średniego i niskiego napięcia
PublicationW artykule przedstawiono metodę wspomagającą decyzje w zakresie wyboru wariantu przyłączenia odbioru do sieci elektroenergetycznej dystrybucyjnej niskiego napięcia lub średniego napięcia oraz mikrogeneracji do sieci niskiego napięcia. Metodę tą zaimplementowano w skoroszycie kalkulacyjnym Microsoft Excel i zastosowano do analizy złożonych przypadków przyłączenia odbioru lub mikrogeneracji.
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On analytical solution of stationary two dimensional boundary problem of natural convection
PublicationApproximate analytical solution of two dimensional problem for sta- tionary Navier-Stokes, continuity and Fourier-Kirchho equations describ- ing free convective heat transfer from isothermal surface of half innite vertical plate is presented. The problem formulation is based on the typ- ical for natural convection assumptions: the uid noncompressibility and Boussinesq approximation. We also assume that orthogonal to the plate component...
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Is It Right To Predict Cutting Forces On The Basis Of Wood Density?
PublicationSeveral properties of wood can be correlated to wood density. It is widely accepted that the cutting power requirements are following this general assumption. Therefore, according to classic literature sources available for determination of the cutting power for both band- and circular- sawing machines, the cutting power requirements (and/or cutting forces) are computed as a function of the wood specific gravity SG. It was shown...
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ROBOT TYPU QUADROCOPTER STEROWANY MIKROKONTROLERAMI O NIEWIELKIEJ MOCY OBLICZENIOWEJ
PublicationWspółczesna robotyka rozwija się bardzo dynamicznie. Coraz więcej osób prywatnych i inżynierów konstruuje różnego rodzaju pojazdy mobilne. Dlatego autorzy niniejszego referatu postawili sobie następującą tezę: możliwa jest budowa latającego robota mobilnego na bazie kontrolera o niskiej mocy obliczeniowej oraz prostego regulatora, i podjęli się jej udowodnienia.
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Image Classification Based on Video Segments
PublicationIn the dissertation a new method for improving the quality of classifications of images in video streams has been proposed and analyzed. In multiple fields concerning such a classification, the proposed algorithms focus on the analysis of single frames. This class of algorithms has been named OFA (One Frame Analyzed).In the dissertation, small segments of the video are considered and each image is analyzed in the context of its...
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N-doped mesoporous carbon nanosheets obtained by pyrolysis of a chitosan–melamine mixture for the oxygen reduction reaction in alkaline media.
PublicationBy simple thermal decomposition of low-cost precursors (chitosan, melamine) in an inert atmosphere, nitrogen-doped porous carbonaceous materials were prepared. The samples pyrolyzed at 700 C are composed of mainly mesoporous nitrogen-doped carbon nanosheets and partially graphitized carbon. The nanosheets contain a disordered area due to the strain imposed by the presence of nitrogen and/or oxygen groups in their structure. Some...
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Health System Efficiency in European Countries: Network Data Envelopment Analysis Approach
PublicationPurpose: The article's main aim is to investigate the effectiveness of health systems in European countries based on EUROSTAT data. A comparative analysis of the health systems' effectiveness in different countries is based on their improvement (reform), using the best practices approach. Design/Methodology/Approach: The network DEA model and a slack-based model (NDEA – SBM) are used. A non-oriented model is used. The research...
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Methodology for determination of the selected mechanical properties of wood based on cutting tests
PublicationFrom kiln-dried spruce wood (with steam) as well as in natural conditions were randomly selected 8 samples. After determining the average dimensions, moisture content and density of the samples they have been cut on the frame sawing machine PRW15M for measurement of cutting power. Based on those results from a linear rela-tionship of cutting power versus feed per toot mechanical properties of wood such as facture toughness and...
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A Broadband Circularly Polarized Wide-Slot Antenna with a Miniaturized Footprint
PublicationThis letter presents a novel and simple feeding technique for exciting orthogonal components in a wide-slot antenna. In this technique, a rectangular bracket-shape parasitic strip is placed at the open end of the straight microstrip line to excite the fundamental horizontal and vertical components of the circular polarization (CP). The proposed technique—when employed in conjunction with the asymmetrical geometry of coplanar waveguide...
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Deep Instance Segmentation of Laboratory Animals in Thermal Images
PublicationIn this paper we focus on the role of deep instance segmentation of laboratory rodents in thermal images. Thermal imaging is very suitable to observe the behaviour of laboratory animals, especially in low light conditions. It is an non-intrusive method allowing to monitor the activity of animals and potentially observe some physiological changes expressed in dynamic thermal patterns. The analysis of the recorded sequence of thermal...
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Minimizing Distribution and Data Loading Overheads in Parallel Training of DNN Acoustic Models with Frequent Parameter Averaging
PublicationIn the paper we investigate the performance of parallel deep neural network training with parameter averaging for acoustic modeling in Kaldi, a popular automatic speech recognition toolkit. We describe experiments based on training a recurrent neural network with 4 layers of 800 LSTM hidden states on a 100-hour corpora of annotated Polish speech data. We propose a MPI-based modification of the training program which minimizes the...
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Pool boiling of nanofluids on rough and porous coated tubes: experimental and correlation
PublicationThe paper deals with pool boiling of water-Al2O3 and water- Cu nanofluids on rough and porous coated horizontal tubes. Commercially available stainless steel tubes having 10 mm outside diameter and 0.6 mm wall thickness were used to fabricate the test heater. The tube surface was roughed with emery paper 360 or polished with abrasive compound. Aluminium porous coatings of 0.15 mm thick with porosity of about 40% were produced by...